Ensure the door isn't in "Vacation" or "Lock" mode when it won't respond to the remote from the outside. When in one of these modes it may open once using the remote, then must be unlocked from the wall control inside the garage.
Click the remote as you are standing under the box but can still see the top. If you can see that the red light on top is blinking, it means that the battery is fine and that the problem exists somewhere else in the system.
Check the battery in your remote operator by walking into the garage holding it in your hand. Press the button as you observe a small blinking red light on the box where the chain enters and exits. If the door opens as you get very close to the box, but fails to open as you back away, the battery is low and needs to be replaced. When you can't see any blinking red light at all on top the box, the battery is dead
Hold the remote in one hand. Grab the wires a few inches back from their connection points with the other hand. Wiggle the wires one by one while pressing the remote switch with the other hand. If one of the wires is loose, when you wiggle it, it will cause the door to open. Identify the wire. Shut off the power to the garage door opener. Use a screwdriver to tighten the wire. Turn the power back on and the door should open and close normally
Locate the fine wires that run away from the control box on the ceiling. There are several inspection points, two run from the box to the manual switch on the wall -- most likely by the walk-in door, and four running from the back of the box to the electric eye locations on both sides of the door a few inches off the floor.